Problem: Find the distance between the points (-3, -2) and (-8, 1). {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} (-3, -2) (-8, 1) $5$ $3$
Solution: Change in $x$ -3 (-8) Change in $y$ (-2) The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{5^2 + 3^2}$ $= \sqrt{34}$